PHP algorithm to generate all combinations of a specific size from a single set

Question

I am trying to deduce an algorithm which generates all possible combinations of a specific size something like a function which accepts an array of chars and size as its parameter and return an array of combinations.

Example: Let say we have a set of chars: Set A = {A,B,C}

a) All possible combinations of size 2: (3^2 = 9)

AA, AB, AC BA, BB, BC CA, CB, CC 

b) All possible combinations of size 3: (3^3 = 27)

AAA, AAB, AAC, ABA, ABB, ACC, CAA, BAA, BAC, .... ad so on total combinations = 27 

Please note that the pair size can be greater than total size of pouplation. Ex. if set contains 3 characters then we can also create combination of size 4.

EDIT: Also note that this is different from permutation. In permutation we cannot have repeating characters for example AA cannot come if we use permutation algorithm. In statistics it is known as sampling.

Answer 1

I would use a recursive function. Here's a (working) example with comments. Hope this works for you!

function sampling($chars, $size, $combinations = array()) {      # if it's the first iteration, the first set      # of combinations is the same as the set of characters     if (empty($combinations)) {         $combinations = $chars;     }      # we're done if we're at size 1     if ($size == 1) {         return $combinations;     }      # initialise array to put new values in     $new_combinations = array();      # loop through existing combinations and character set to create strings     foreach ($combinations as $combination) {         foreach ($chars as $char) {             $new_combinations[] = $combination . $char;         }     }      # call same function again for the next iteration     return sampling($chars, $size - 1, $new_combinations);  }  // example $chars = array('a', 'b', 'c'); $output = sampling($chars, 2); var_dump($output); /* array(9) {   [0]=>   string(2) "aa"   [1]=>   string(2) "ab"   [2]=>   string(2) "ac"   [3]=>   string(2) "ba"   [4]=>   string(2) "bb"   [5]=>   string(2) "bc"   [6]=>   string(2) "ca"   [7]=>   string(2) "cb"   [8]=>   string(2) "cc" } */ 

Answer 2

A possible algorithm would be:

$array_elems_to_combine = array('A', 'B', 'C'); $size = 4; $current_set = array('');  for ($i = 0; $i < $size; $i++) {     $tmp_set = array();     foreach ($current_set as $curr_elem) {         foreach ($array_elems_to_combine as $new_elem) {             $tmp_set[] = $curr_elem . $new_elem;         }     }     $current_set = $tmp_set; }  return $current_set; 

Basically, what you will do is take each element of the current set and append all the elements of the element array.

In the first step: you will have as result ('a', 'b', 'c'), after the seconds step: ('aa', 'ab', 'ac', 'ba', 'bb', 'bc', 'ca', 'cb', 'cc') and so on.